Sentence examples for concise formulae from inspiring English sources

A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods.

This paper presents a new form of quartic equation with Lagrange's extremum law and a Groebner basis technique, and seeks a very explicit and concise formulae of the quartic equation by Ferrari's line.

The information obtained in this way is incorporated in a concise formula, which is known as the individual's fingerprint classification.

This is supposed to be a metaphor for reducing reality to a concise formula.

Furthermore, through asymptotic analysis, we derive concise formulas and show how the optimal parameter values roughly behave as functions of number of tags N and confidence level α.

Accuracy is verified by comparing the concise formulas' calculation results with the simulation results and practical operation data under different load control strategies.

A concise formula was used, with empirical algorithm as the constraint of optimization design, to locate the optimal cooling time and the required optimal geometric factor constraints.

In Section 6, we establish concise formulas through asymptotic analysis and investigate the asymptotic behavior of the optimal parameter values as functions of number of tags N and confidence level α.

Theology's subject is the object of belief "in so far as the believable is transformed into the notion of the intelligible, and this happens by the addition of reasoning".[12] With this concise formula, Bonaventure includes within theology both religious belief transformed by arguments from natural reason and natural reason transformed by arguments based on religious revelation.

Additionally, through asymptotic analysis, we obtained concise formulas which demonstrate: (1) the optimal frame size increases linearly as a function of number of tags, and (2) the optimal termination time increases logarithmically, either as a function of number of tags or as a function of 1/ε (where ε stands for level of identification failure).

However, the expression given in Eq. 20 is not in a convenient form for auxiliary channel selection; a concise formula in terms of matrix determinants is derived as follows: The middle term in Eq. 20 is denoted with G T and is expressed as: {mathbf{G}_{T}} = mathbf{V}_{T}^{H}{mathbf{V}_{T}} + {mathbf{Phi }_{I}} (21).